Pre-Algebra Examples

$\sqrt{{(100)}^{2} + {(100)}^{2}}$

Step 1

Raise $100$ to the power of $2$ .

$\sqrt{10000 + {(100)}^{2}}$

Step 2

Raise $100$ to the power of $2$ .

$\sqrt{10000 + 10000}$

Step 3

Add $10000$ and $10000$ .

$\sqrt{20000}$

Step 4

Rewrite $20000$ as $100^{2} \cdot 2$ .

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Step 4.1

Factor $10000$ out of $20000$ .

$\sqrt{10000 (2)}$

Step 4.2

Rewrite $10000$ as $100^{2}$ .

$\sqrt{100^{2} \cdot 2}$

$\sqrt{100^{2} \cdot 2}$

Step 5

Pull terms out from under the radical.

$100 \sqrt{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$100 \sqrt{2}$

Decimal Form:

$141.42135623 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$